As mentioned in class, the story of options and the development of.docx

As mentioned in class, the story of options and the development
of the Black-Scholes formula is intertwined with the story of
international financial markets and investment and global
financial crisis.
Although B-S was originally developed for pricing stock
options, the formula that we have been using in class for
currency options is virtually identical. Specifically, except for
the Tr e − * term that discounts by the foreign interest rate, and
of course the fact that the underlying asset is a foreign currency
rather than a share of stock, the formulas are exactly the same.
In addition to the development of the B-S formula, the video
brings together many concepts that we have seen in class this
semester, including (in no particular order):
- Replicating portfolio and no-arbitrage pricing
- Market efficiency vs. forecasting
- Statistical methods for characterizing returns and measuring
risk -
Risk transfer role of derivatives and hedging - Derivatives
trading and exchanges
- International capital flows and investment
- Currency crisis and contagion
Besides these, the video also gives a great glimpse into the
world of academic finance, the inner workings of financial
markets and institutions, and the nature of financial crises.
While you are watching, note the similarity between what got us
into trouble back then and what got us into trouble today (e.g.,
excessive debt/leverage to fuel a property boom,
underassessment of risk and/or overconfidence in our ability to
deal with risk, government bailouts, etc.).
Extra Credit Assignment Due Tuesday, December 6, 2016
Value: +10 points.
hoose any five (5) of the bullet points above and discuss the
topic further by describing what we learned in class about the
topic and linking it to specific parts of the video in which it is

mentioned or occurs. A two to three paragraph discussion for
each point should suffice, totaling 2-3 pages for the entire
assignment.
https://vimeo.com/28554862
Cognitive Science 28 (2004) 963–977
A developmental shift in processes underlying
successful belief-desire reasoning
Ori Friedmana,∗ , Alan M. Lesliea,b
a Center for Cognitive Science, Rutgers University, 152
Frelinghuysen Road, Piscataway, NJ, USA
b Department of Psychology, Rutgers University, USA
Received 11 March 2004; received in revised form 4 June 2004;
accepted 5 July 2004
Available online 25 September 2004
Abstract
Young children’s failures in reasoning about beliefs and desires,
and especially about false beliefs,
have been much studied. However, there are few accounts of
successful belief-desire reasoning in older
children or adults. An exception to this is a model in which
belief attribution is treated as a process
wherein an inhibitory system selects the most likely content for
the belief to be attributed from amongst

several competing contents [Leslie, A. M., & Polizzi, P.
(1998).Developmental Science, 1, 247–254].
We tested this model with an ‘avoidance false belief task’ in
which subjects predict the behavior of a
character, who wants to avoid an object but who is mistaken
about which of three locations it is in. The
task has two equally correct answers—in seeking to avoid the
location where she mistakenly believes
the object to be, the character might equally go to the location
where the object actually is, or to the
remaining empty location. However, the model predicts that
subjects will prefer one of these answers,
selecting the object’s actual location over the empty location.
This bias was confirmed in a series of
five experiments with children aged between 4 and 8 years of
age. A sixth experiment ruled out two
rival explanations for children’s biased responding. Two further
experiments found the opposite bias in
adults. These findings support one selection model as an
account of belief-desire reasoning in children,
and suggest that a different model is needed for adults. The
process of selecting contents for mental state
attributions shows a developmental shift between 8 years of age
and adulthood.
© 2004 Cognitive Science Society, Inc. All rights reserved.
Keywords: Belief-desire reasoning; Inhibition; Selection
Processing; Theory of mind
Social cognition rests on the ability to reason about other
people’s mental states. A major goal
of research has been to discover how young children come to
reason about beliefs, desires, and
other mental states. Investigation of children’s belief-desire
reasoning has mainly concerned
children’s ability to reason about false beliefs. This ability is

tested with the false belief (FB)
∗ Corresponding author.
E-mail address:[email protected] (O. Friedman).
0364-0213/$ – see front matter © 2004 Cognitive Science
Society, Inc. All rights reserved.
doi:10.1016/j.cogsci.2004.07.001
964 O. Friedman, A.M. Leslie / Cognitive Science 28 (2004)
963–977
task, which requires children to attribute a false belief to
another person or themselves. Children
typically pass the FB task at four but fail at 3 years (for a recent
meta-analysis seeWellman,
Cross, & Watson, 2001).
The cause of young children’s difficulty with the FB task has
inspired intense debate (e.g.,
Scholl & Leslie, 2001). However, while much effort has gone to
discoveringwhy younger
children fail the FB task, little attention has paid tohow
successful belief-desire reasoning
occurs. We remain largely ignorant about the cognitive
processes of children who succeed in
belief-desire reasoning, and equally ignorant about these
processes in adults.
We test the first detailed account of successful belief-desire
reasoning (Leslie, 2000; Leslie &
Polizzi, 1998). We replicate and extend previous findings that
support the model as an account
of children’s belief-desire reasoning (Friedman & Leslie, 2004).

We then provide evidence
against the model as an account of belief-desire reasoning in
adults. Our findings suggest
a developmental shift between middle childhood (or later) and
adulthood in the processes
underlying belief-desire reasoning. We begin by reviewing
findings that led to the development
of the model, and then describe the model itself.
1. Approach and avoidance FB tasks
There is a striking contrast between children’s performance on
two versions of the FB task.
In standard FB tasks (Baron-Cohen, Leslie, & Frith, 1985;
Wimmer & Perner, 1983), children
view a scenario in which a girl, Sally, wants to obtain a frog,
sees it go under a red box, but is
absent when the frog moves to under a blue box. Children are
asked either where Sally thinks
the frog is (Think question), or where she will look for the frog
(Prediction question). Both
questions have the same correct answer: Sally thinks the frog is
in the red box and will look for
the frog in this location. We will refer to the red box as the
false belief location (FB-Location)
because by indicating this location, the child correctly attributes
a false belief to Sally. We refer
to the blue box as the true belief location (TB-Location)
because by indicating this location the
child mistakenly attributes a true belief. Both questions are
equally difficult, passed by most
children at 4 years, failed by most at three.
In avoidanceFB tasks, the protagonist wants to avoid the object
about which a false belief
is held. Suppose that Sally wants to put her clean hat away in a

box, and wants to avoid
putting it in the box with the frog. Children are again asked a
Think question, and a slightly
different Prediction question, “Which box will Sally go to with
her clean hat?” In the avoidance
FB task the Think and Prediction questions have different
answers: Sally wants to avoid the
FB-Location, where she falsely believes the frog to be, and so
she will mistakenly go to the
TB-Location, where the frog actually is. In contrast to approach
FB tasks, the Think and
Prediction questions in avoidance tasks differ greatly in
difficulty. Four-year-olds who pass the
Think question mostly fail the Prediction question (Cassidy,
1998; Leslie, German, & Polizzi,
in press; Leslie & Polizzi, 1998).
Why do FB task passers fail to predict behavior in avoidance FB
tasks? Failure does not
result from difficulty understanding that people can have
avoidance desires, because even 3-
year-olds can reason about avoidance desire in the context of
true belief (Cassidy, 1998; Leslie,
Friedman, & German, in press). In addition, failure does not
result because avoidance desire
O. Friedman, A.M. Leslie / Cognitive Science 28 (2004) 963–
977 965
increases thegeneraldifficulty of the FB task: the need to
consider avoidance desire does not
increase the difficulty of prediction in a matched ‘partial
knowledge’ control task (Friedman
& Leslie, in press).

2. Selection Processing
To account for the difficulty of behavior prediction in the
avoidance FB task,Leslie and
Polizzi (1998)extended the Selection Processing account
developed by Leslie and colleagues
(Leslie & Thaiss, 1992; Roth & Leslie, 1998). The Selection
Processing account claims that,
in belief-desire reasoning tasks, children’s main challenge is to
select the correct target of
the character’s belief or action from amongst several plausible
candidates. In the FB task, for
example, children must try to select the correct target of Sally’s
belief about where the frog is
from two plausible targets—the TB- and FB-Locations.
Selection has two stages. First, an unconscious “theory of mind
mechanism” (ToMM) rep-
resents plausible candidate contents for the belief or desire to
be attributed. Then an inhibitory
process selects the most plausible candidate (Leslie & Thaiss,
1992; Roth & Leslie, 1998).
Selection operates under the following rules:
1. The salience of candidate contents varies by degree and
contents can have their salience
decreased by inhibition.
2. Among the contents, typically one is true, the true-belief
content. Initially, the true-belief
content is most salient and will be selected by default.
3. For success in a FB task, the TB content must be inhibited so
that its salience falls below
that of the false-belief content.

4. Predicting the behavior of a character with an avoidance
desire, the to-be-avoided target
is identified and then inhibited so that an alternative target is
selected.
Most 3-year-olds can predict behavior if an avoidance desire is
in the context of a true-belief,
suggesting that less inhibition is necessary to determine the
target of an avoidance desire than
to determine the target of a false-belief (seeLeslie, Friedman, et
al., in press; Leslie, German,
et al., in pressfor further details).
The Selection Processing account explains key findings from
research on children’s belief-
desire reasoning: 3-year-olds typically fail FB tasks because
they lack the processing resources
to inhibit the true-belief. True belief attribution is easy because
it does not require the default
to be inhibited. Some task manipulations, which ease 3-year-
olds’ difficulty with false belief,
operate by reducing the salience of the true-belief (seeLeslie,
Friedman, et al., in press; Leslie,
German, et al., in press; Surian & Leslie, 1999). In claiming
that success in FB tasks requires in-
hibitory processing, the Selection Processing model is related to
other accounts of belief-desire
reasoning (e.g.,Carlson, Moses, & Breton, 2002; Russell,
Mauthner, Sharpe, & Tidswell, 1991).
3. Selection Processing in avoidance FB tasks
According to the Selection Processing account, behavior
prediction in avoidance FB tasks is
difficult because it requires ‘double inhibition,’ with one

inhibition required for false belief and
963–977
another for avoidance desire. If both inhibitions are simply
combined and both applied to the
true-belief content – because it is the default beliefandthe to-be-
avoided target – then the false-
belief and thus the FB-Location will be selected as target of the
character’s action. However,
this is the wrong answer in this task.Leslie and Polizzi
(1998)suggested two different ways that
double inhibitions could combine to select the correct answer.
One of these, the “Inhibition of
Return” model, has recently been ruled out as an account of
children’s belief-desire reasoning
(Friedman & Leslie, 2004; Leslie, Friedman, et al., in press;
Leslie, German, et al., in press),
while the other, the “Inhibition of Inhibition” model, has
received support. Therefore, we will
describe only the latter.
4. The Inhibition of Inhibition model
According to the Inhibition of Inhibition (IOI) model, for
successful prediction in the avoid-
ance FB task, inhibitions for belief and desire are applied in
parallel so that they inhibit each
other and cancel out. Because no inhibition reaches the true-
belief target, it remains salient.
Thus, the TB-Location is correctly selected as the target of the
character’s action.Fig. 1depicts
the operation of this model in the course of predicting behavior

in the avoidance FB task.
We can test the IOI model of Selection Processing by adding a
third location (Neutral-
Location) to the avoidance FB task. With three locations, the
task has two equally correct
answers: In seeking to avoid the FB-Location Sally is equally
likely to go to either the TB- or
Neutral-Location. However, the IOI model predicts that children
who pass will be biased to
select the TB-Location over the Neutral-Location: Inhibitions
for false belief and avoidance
desire are applied to the true-belief in parallel, but cancel out
without modifying its salience.
The TB-Location, therefore, remains most salient, and is
selected as the target of Sally’s action.
Friedman and Leslie (2004)report an experiment confirming the
above prediction. Here we
seek to replicate this finding, using a wider range of materials
and age groups, including adult
subjects. We begin by testing whether children who pass the 3-
Location avoidance FB task
Fig. 1. The Inhibition of Inhibition model of Selection
Processing. The representations of the TB- and FB-Locations
are shown as boxes. Selection is illustrated by way the arrow or
index, which points at the currently most salient
candidate. To predict where a character with a false belief and
an avoidance desire will go: (1) The true belief
content is initially most salient. (2) Inhibitions for false belief
and avoidance desire are applied in parallel, such that
they cancel each other out. (3) The true belief content remains
most salient, and so the TB-Location is selected as
the target of the character’s action.

977 967
have a bias to select the TB-Location over the Neutral-Location.
We investigated this question
in a series of five experiments that differ only in the details of
the avoidance FB task used, and
in the ages of the children tested. We present these five
experiments together—both to ease
comparisons between the experiments, and for brevity.
5. Experiments 1–5
Across five experiments, children were presented with three
different versions of the avoid-
ance FB task. In Experiments 1 through 3 we used three
different versions of the avoidance FB
task, with children who were mostly four and five. Experiment 4
tested slightly older children,
and in Experiment 5 we tested 7- and 8-year-olds.
The IOI model predicts that children who pass the 3-Location
avoidance FB task will predict
that the character will go to the TB-Location. This prediction
concerns children whosucceed
and so we only wanted to examine responses of reliable passers,
not of children who pass
by lucky guesses. To ensure that we were dealing with reliable
passers, we only analyzed
responses from children who passed all questions in the 3-
Location avoidance FB task, and in
a 2-Location FB task administered as a screen. The screening
task was not used in Experiment
5 because children were seven and eight and assumed to be

reliable passers.
5.1. Method
5.1.1. Subjects
In Experiment 1, 36 of 57 children passed all control (Memory,
Reality, and Think) questions,
but 28 of these children failed a Prediction question, leaving 8
reliable passers. In Experiment
2, 13 of 20 children passed all control questions, but 6 of these
failed a Prediction question,
leaving 7 reliable passers. In Experiment 3, 25 of 46 children
passed all control questions, but 15
of these children failed a Prediction question, leaving 10
reliable passers. In Experiment 4, 13
of 17 children passed all control questions, but 4 of these
children failed a Prediction question,
leaving 9 reliable passers. In Experiment 5, control questions
were passed by all 9 children
tested, but one failed a Prediction question, leaving 8 reliable
passers. Detailed information
about children’s ages in each experiment is provided inTable 1,
which displays the average
age and age range of all children tested, of control question
passers, and of reliable passers.
5.1.2. Materials
All tasks made use of a foam board stage, differently colored
boxes, and props used to enact
the tasks. In Experiments 1–4, all materials differed between the
two tasks administered, except
for the stage.
5.1.3. Procedure

In Experiments 1 through 4, each child received a 3-Location
avoidance FB task and a
2-Location version. Tasks were presented in counterbalanced
order, except in Experiment 2
where the 3-Location task was always presented first. In
Experiment 5, children only received
the 3-Location task.
963–977
Table 1
Mean age and age range of all children tested, of children who
passed all control questions, and of reliable passers,
in Experiments 1–5
Experiment Group N Mean age (SD) Age range
1 All children 57 58.1 (7.3) 44–77
Control passers 36 60.1 (7.3) 45–77
Reliable passers 8 59.8 (8.8) 49–77
2 All children 20 59.0 (6.14) 49–70
3 All children 46 58.0 (8.1) 43–74
4 All children 17 65.5 (11.9) 52–99
Control passers 13 68.9 (11.6) 55–99

5 All children 9 95.7 (7.7) 85–107
Several similar storylines were used to enact the tasks.
Appendix 1 shows the storyline and
protocols for the 3-Location version of the avoidance FB task
used in Experiment 1. All tasks
involved a character who wants to put an item in one of three
boxes, but not with an animal.
In 2-Location tasks, the character saw the animal under one box
(FB-Location) but was absent
when the animal moved to under another box (TB-Location).
Three different versions of the
3-Location task were used—seeFig. 2 for a visual summary.
5.1.3.1. Experiment1.The character first saw the animal under a
box at the right or left end of
the row of boxes (FB-Location), but was absent when the
animal temporarily moved to under
the middle box (Neutral-Location) and then moved to the final
box (TB-Location).
5.1.3.2. Experiment2.The character first saw the animal under
the middle box (FB-Location)
but was absent when it moved to under an end box (TB-
Location). The Neutral-Location, the
other end box, was never visited.
5.1.3.3. Experiments 3–5.The character first saw the animal
under one end box (Neutral-
Location), then saw the animal move to under the middle box
(FB-Location), and was absent
when the animal moved to the other end box (TB-Location).

Following presentation of each task scenario, children were
asked Memory, Reality, and
Think control questions, and a Prediction question.1 Experiment
2 also included a Know
control question asked prior to the Think Control question. To
pass the Prediction question in
2-Location tasks children had to pick the TB-Location. To pass
Prediction in 3-Location tasks,
children could select either the TB-Location or the Neutral-
Location or both.
977 969
Fig. 2. Versions of the 3-Location avoidance FB task used in
Experiments 1–5.
Direction of the animal’s motion was counterbalanced: For half
of the children in each
experiment, the animal moved from the right to the left in the 3-
Location task and from the
left to the right in the 2-Location task. Direction of movement
was reversed for the remaining
children.
5.2. Results
In each experiment, reliable passers were biased to select the
TB-Location over the Neutral-
Location in response to the Prediction question in the 3-
Location avoidance FB task. In Experi-
ment 1, 7 (87.5%) of 8 reliable passers selected the TB-
Location, and one selected both correct
answers and was conservatively scored as selecting the Neutral-

Location (Binomial sign test,
N = 8,x = 1,p = .035, one-tailed). In Experiment 2, all seven
(100%) reliable passers selected
the TB-Location (Binomial,N = 7,x = 0,p = .008). In Experiment
3, 8 (80.0%) of 10 reliable
passers selected the TB-Location, one selected the Neutral-
Location, and one selected both
correct answers and was conservatively scored as selecting the
Neutral-Location (Binomial,
N = 10,x = 2, p = .055, one-tailed). In Experiment 4, 8 (89%) of
9 reliable passers selected
the TB-Location, and one indicated the Neutral-Location
(Binomial,N = 9, x = 1, p = .02,
one-tailed). In Experiment 5, 7 (87.5%) of 8 reliable passers
selected the TB-Location, and
the remaining child selected the Neutral-Location (Binomial
sign test,N = 8, x = 1, p = .035,
one-tailed).
Summing across the five experiments, there were 42 reliable
passers and 37 (88.1%) se-
lected the TB-Location (p < .0001, one-tailed).Table
2summarizes these results. When we
included non-reliable passers, the same bias remained: counting
children who passed all Con-
trol questions and the Prediction question in the 3-Location task
(but who may have failed
963–977
Table 2
Reliable passers selecting the TB- and Neutral-Locations in
Experiments 1–5

Experiment TB-Location Neutral-Location or both answers
1 7 1
2 7 0
3 8 2
4 8 1
5 7 1
Combined 37 5
Prediction in the 2-Location task), 84% chose the TB-Location
(Binomial,N = 49,x = 8, p <
.0001, one-tailed).
5.3. Discussion
Children who passed the 3-Location avoidance FB task were
biased in answering the
Prediction question. In all five experiments, children more often
selected the TB-Location
over the Neutral-Location, though both answers are equally
correct. The IOI model pre-
dicted this bias and we were able to replicate and extend the
findings ofFriedman and Leslie
(2004).
Biased responding was found using three different versions of
the 3-Location avoidance
FB task, suggesting that the bias is robust. Had we only
administered one version of the task,
then it might have appeared that the bias was an artifact specific
to that version of the task. For
example, in Experiment 1 the Neutral-Location was always the
middle box in the row of boxes,
and the TB-Location always an end box. Biased responding in

this version of the task might
result from some spatial bias that made the middle box less
salient than those at the ends of
the row. However, in the remaining experiments both correct
locations were end boxes, ruling
this explanation out.
We next tested two rival explanations for children’s bias to
select the TB-Location. Children
might have followed anObject Biasand selected the TB-Location
because it contained an
animal whereas the Neutral-Location was empty. Alternatively,
children may have aFail-
ure Bias and may have selected the TB-Location, because that
location would frustrate
the character’s desire to avoid the animal. AlthoughFriedman
and Leslie (2004)have sup-
ported the IOI model of Selection Processing over these rival
explanations, we sought further
evidence.
To test the rival explanations, we devised an avoidance
Ignorance task: Sally wants to put
her clean hat away under one of two boxes so that she can keep
her hat clean. After confirming
that both boxes are empty, she goes to get her hat. During her
absence, a dirty frog enters
and children are asked whether Sally would want to put her
clean hat with the dirty frog. The
frog then goes under one box (Object-Location) with the other
left empty (Neutral-Location).
Children are then asked whether Sally knows that there is a frog
in the Object-Location (Know
question), followed by a Prediction question. In this task, Sally
has no belief about the location
of the frog because she has never seen it.

977 971
Like the 3-Location avoidance FB task, the avoidance Ignorance
task has two equally correct
answers about where the character will go—a location holding
an object that the character
would want to avoid, and an empty location. Both rival
explanations predict that children will
select the Object-Location, because it contains an object (Object
Bias), or because it frustrates
Sally’s desire to avoid a dirty location (Failure Bias).
The IOI model, in contrast, predicts no bias in the avoidance
Ignorance task. Recall that the
model is a model of successful performance. To succeed in this
task, there should be no index
for a belief about the frog because Sally does not have any
belief about the frog. When asked
to predict her action, an index for desire should be attracted to
whichever target is the more
salient. Because there is no principled reason for one target to
be more salient than another,
the index should go to either target about equally. There may be
extraneous factors that boost
one target over the other (a favorite color, for example), but if
such factors play any role, they
are outside the scope of the model. The main point is that, in
contrast to the Object and Failure
biases, the IOI model does not predict the same bias for the
avoidance Ignorance task that it
predicted for the avoidance FB task.

As in the previous experiments, we were interested in the
responses of reliable passers, and
so the avoidance Ignorance task was followed by a 2-Location
avoidance FB task that served
as a screen.
6. Experiment 6
6.1. Method
6.1.1. Subjects
Eleven children, between 5:5 and 6:3, mean = 5:11 years,SD =
2.84 months, completed
the experiment. One child was rejected for failing the Prediction
question in the 2-Location
avoidance FB screening task. The remaining 10 children ranged
between 5:5 and 6:3 (mean =
5:11,SD= 2.91 months).
6.1.2. Procedure
Children received the avoidance Ignorance task followed by a 2-
Location avoidance FB task.
This fixed order was used to ensure that performance on the
Ignorance task was not biased by
performance in the avoidance FB task. For half of the children
the Object-Location was on the
right and the Neutral-Location on the left, with sides reversed
for the remaining children.
6.2. Results
Children in the avoidance Ignorance task showed no bias to
select one location over the other.
Of 10 children, 7 selected the Neutral-Location and 3 selected

the Object-Location (Binomial,
N = 10,x = 3, p = .34, two-tailed). Children’s performance in
this task differed significantly
from that in the avoidance FB tasks of the previous experiments
(Fisher’s Exact,p = .001,
two-tailed).
963–977
6.3. Discussion
The avoidance Ignorance task has two equally correct answers
about where the character
will go—a location containing an object to be avoided and an
empty location. If children in the
previous avoidance FB tasks had Object or Failure biases, then
in the present task they should
also have been biased to select the Object-Location over the
Neutral-Location. Running counter
to this, if anything, slightly more children selected the Neutral-
Location. This finding rules out
Object and Failure biases as accounts for children’s bias in the
avoidance FB task.
Were children actually biased toward the Neutral-Location?
Even on a one-tailed test, we
cannot support that statement on present results. However,
suppose some children actually
index the frog’s location, as if Sally knew about the frog. This
would be an error, of course,
reflecting a “curse of knowledge.” Such children might then
inhibit that location because of the
avoidance desire and predict that Sally will go to the Neutral-

Location. We cannot tell from
present results which children, if any, followed this scenario, so
it is a topic for future research.
Having supported the IOI model over the rival explanations, we
next investigated the 3-
Location avoidance FB task in adults. Are adults also biased to
select the TB-Location over
the Neutral-Location?
Although adults may readily perceive both correct answers,
sensitive tests may reveal biases
produced by underlying reasoning processes, as shown in a
number of cases (e.g.,Gigerenzer,
Todd, & ABC Group, 1999; Tversky & Kahneman, 1974),
including social reasoning (Camerer,
Loewenstein, & Weber, 1989) and even belief-desire reasoning
(Mitchell, Robinson, Isaacs,
& Nye, 1996). Pilot testing indicated that the dolls and props
used in testing children were too
‘babyish’ for use with adults. Thus, we presented adults with
the 3-Location avoidance FB task
in cartoon form. Because we assumed that, unlike children, it
would be obvious to adults that
the task had two correct answers, we asked adults to pick the
first answer that came to mind.
We tested adults in two experiments. The experiments only
differed slightly and so we present
them together.
7. Experiments 7 and 8
7.1. Method
7.1.1. Subjects
Thirty adults were tested in Experiment 7, though five were

rejected from analysis for failing
the Prediction question and selecting the FB-Location. An
additional 30 adults were tested in
Experiment 8, and 4 were rejected for failing the Prediction
question. In both experiments, all
subjects were undergraduate students at Rutgers University and
aged between 18 and 22 years.
7.1.2. Materials
Subjects received an instruction sheet and a cartoon depicting a
3-Location avoidance FB
task. In Experiment 7 the cartoon depicts Mike who owns three
identical sheds lined in a row.
He sees his cat jump into one shed (FB-Location) but is absent
when it jumps into another
shed. A frame below the main cartoon instructs subjects to
indicate which shed Mike will go to
977 973
upon returning, given a desire to go to an empty shed. A sample
cartoon appears in Appendix
2.
In Experiment 8, Mike has three cottages that he rents out. He
sees a lizard crawl under the
door of one cottage (FB-Location) and goes away to call the
exterminator. During his absence,
the lizard crawls into another cottage (TB-Location) and Mike
meets a couple who want to
rent out a cottage. Subjects were instructed to indicate which

cottage Mike gives the couple
keys for, given that he does not want to rent out the cottage
containing the lizard.
Half of the cartoons in each experiment showed the animal
moving from the middle location
to the end location on the right, and the other half showed the
animal moving to the end location
on the left.
7.1.3. Procedure
Subjects were told that they would look over a cartoon and then
answer a question about it
on paper. Subjects were told that the question might have more
than one correct answer, and
that they should pick the first correct answer that came to mind.
7.2. Results
Subjects were biased to select the Neutral-Location over the
TB-Location. In experiment 7,
25 subjects selected a correct answer, of whom 22 (88%) picked
the Neutral-Location and 3
picked the TB-Location (Binomial,N = 25,x = 3,p < .0002, two-
tailed). In Experiment 8, 26
subjects selected a correct answer, of whom 22 (84.6%) selected
the Neutral-Location and 4
selected the TB-Location (Binomial,N = 26,x = 4,p < .0003,
one-tailed).
7.3. Discussion
When giving the first answer that came to mind, adults were
biased when predicting a
character’s behavior in the 3-Location avoidance FB task.

However, the adult bias was toward
the Neutral-Location—the opposite to that found in children.
After finding biased responding in Experiment 7, we worried
that the bias might have resulted
from an ambiguity in the Prediction question. Though we had
intended subjects to indicate the
first shed they thought Mike would go to, subjects may have
wondered whether we were asking
about where Mike would go eventually. They may have selected
the Neutral-Location, then,
because it is the only answer correct under both interpretations
of the question. Experiment
8 was designed to avoid such ambiguity—it is clear that the
question concerns the cottage
key that Mike first gives the renters, and not whichever key he
might later give them if they
complain about the lizard in their cottage. However, the results
were the same.
Adults were instructed to select the first correct answer that
came to mind. This instruction
was not given to children in Experiments 1 through 6. It is
possible that children would have
performed differently if they had received this instruction, or
that adults would have performed
differently if they had not. We are skeptical about this, although
it is an empirical question and
will need to be resolved in future experiments. The main reason
we gave the instruction to adults
was that in pilot studies adults took a long time before
answering the Prediction question. We
feared that perhaps adults were looking for hints as to whether
one of the correct answers was

963–977
somehow better, and that a prolonged effortful search would not
reflect heuristic processing.
Children did not show similar hesitation and therefore were not
given the instruction. We
assume that Selection Processing is a heuristic process (Leslie,
Friedman, et al., in press;
Leslie, German, et al., in press).
8. General discussion
The IOI model of Selection Processing provides the most
detailed account to date of the role
of inhibitory processing in the FB task and of how belief-desire
reasoning operates. The model
claims that successful attribution of false belief requires
inhibitory processing to overcome a
default tendency to attribute true belief (from the attributer’s
point of view). The model claims
that inhibition is also necessary when predicting the behavior of
a person with an avoidance
desire, because predicting where the person will go requires
first inhibiting what the person will
avoid. Predicting behavior in the case of avoidance FB therefore
requires ‘double inhibition’ and
is more difficult than tasks involving single inhibition, like
standard false belief or avoidance
desire with true belief, or no inhibition, like true belief with
approach desire. The model
claims that, in ‘double inhibition,’ inhibitions for belief and
desire cancel out without other
effect, leaving the true-belief content uninhibited. The model
therefore predicts that subjects

succeeding in the 3-Location avoidance FB task will be biased
to select the TB-Location as
the target of the character’s action, even though the Neutral-
Location is equally correct. As far
as we know, the IOI model is the only account of children’s
belief-desire reasoning to make
anyprediction about performance in the 3-Location avoidance
FB task.
We tested the IOI model in children and adults. Children who
passed the avoidance FB task
were biased to select the TB-Location over the equally correct
Neutral-Location (Experiments
1 through 5), replicating previous findings (Friedman & Leslie,
2004). Object and Failure biases
were ruled out as possible explanations for children’s bias to
select the TB-Location—both of
these rival accounts predicted that children should prefer the
‘Object-Location’ in the avoid-
ance Ignorance control task, but this was not found (Experiment
6). Thus, the findings from
Experiments 1 through 6 support the IOI model as an account of
belief-desire reasoning in
children.
Adults who passed the 3-Location avoidance FB task showed
the opposite bias to children,
and selected the Neutral-Location. This finding conflicts with
the IOI model, and so a different
account is needed to explain this. We might explain the adult
bias with a different Selection
Processing model, namely, the Inhibition of Return model
(Leslie & Polizzi, 1998). This model
has already been ruled out for children’s belief-desire reasoning
(Friedman & Leslie, 2004;
Leslie, Friedman, et al., in press; Leslie, German, et al., in

press) and is further contradicted
by Experiments 1 through 5. In the Inhibition of Return (IOR)
model, Selection Processing
involves two distinct indexes, one to attribute belief and the
other to predict behavior, and
inhibitions for belief and desire are applied serially rather than
in parallel. AsFriedman and
Leslie (2004)point out, the IOR model predicts a Neutral-
Location bias in a 3-Location avoid-
ance false belief task. It is possible, then, that IOR may capture
adult heuristic belief-desire
reasoning. We remain tentative on the question of whether IOR
is a good model for adults
pending further evidence. However, we might speculate that
age-related increases in process-
977 975
ing resources may allow a more sophisticated heuristics in
which belief and desire are indexed
and inhibited separately (seeLeslie, Friedman, et al., in press;
Leslie, German, et al., in press
for further discussion of this model).
Other accounts might also explain the adult bias. For example,
responding may have resulted
from a bias towards granting the character’s desire, or from ‘the
curse of knowledge’ (Birch &
Bloom, 2003; Camerer et al., 1989) or ‘epistemic egocentrism’
(Roysman, Cassidy, & Baron,
2003). Perhaps adults are far more prone to these errors than are
children. These are excellent
topics for future research.

Whatever the explanation, the difference between response
biases in children and adults is
startling. Developmental changes in belief-desire reasoning
usually involve improvement with
age (for an important exception, seeMitchell et al., 1996).
However, our findings indicate a de-
velopmental change in the processes
underlyingcontinuingsuccessfulbelief-desire reasoning.
An important goal for future research is uncovering the nature
and cause of the developmental
shift in processing we have identified. One goal will be to
discover when children first readily
perceive that the avoidance FB task has two correct answers. In
Experiments 1 through 5, very
few children selected both correct answers, and few selected the
Neutral-Location itself. It is
possible, then, that few children notice that the Neutral-
Location is also correct. If so, then
there may be two shifts between childhood and adulthood—the
shift in biases reported here,
and perhaps a shift from seeing one correct answer to seeing
both.
A second goal will be to discover when the shift between biases
occurs. Based on current
findings, the shift should occur after 8 years but before 18.
Neuroimaging studies have consis-
tently identified the medial prefrontal cortex, especially the
anterior paracingulate, as involved
in processing FB tasks (Frith & Frith, 1999; Gallagher & Frith,
2003). The prefrontal cortex
is thought to be crucial for inhibitory processing with different
regions underlying successful
inhibitory processing in children and adults (Durston et al.,

2002). Furthermore, this region
undergoes major development during puberty (Giedd et al.,
1999). The developmental shift
in belief-desire reasoning we have identified may be produced
by the changes in inhibitory
processing associated with puberty.
Notes
1. In Experiment 1, our second Memory control question in the
3-Location task (“Where
did [animal] go after that?”) was unclear—many children who
otherwise passed pointed
to the final location of the animal. For this reason we did not
eliminate children who
failed this question, but modified it in subsequent experiments:
“Where did [animal] go
right after that?”
Acknowledgments
We thank Amir Amirrezvani for aiding data collection in
Experiment 7, and Dan Sperber,
Peter Mitchell, and two anonymous reviewers for a careful
reading of and helpful comments
on an earlier draft. This work was supported by NSF grant BCS-
0079917 awarded to A.M.L.
963–977
Appendix 1
Protocol for 3-Location FB task used in Experiment 1.

This is Billy and look what he has—it’s a bone! Billy wants to
put this bone away under a
box. So he leaves the bone outside, and he goes into the room to
look for a box to put it under.
And look, there are three boxes here. What color is this box?
What color is this box? And what
color is this box?
Let’s see if there is anything under the boxes. Anything under
the black box? No, nothing.
And under the yellow box? Nothing. And under the green box?
A dog! But it’s a sick dog,
because it’s got a toothache. Billy does not want to put the bone
with the dog because then its
tooth will hurt more.
Now Billy is going to go outside to get the bone, so he can put
it under a box. Why does
Billy not want to put the bone with the dog? Right, because he
doesn’t want its tooth to hurt
more.
Now look what happens while Billy is gone: The dog crawls
from under the green box, and
it goes under the yellow box. And then, the dog crawls from
under the yellow box and crawls
under the black box. Did Billy see that? No!
Now Billy is going to come back with the bone to put it under a
box, and I have some
questions for you. . .
Memory 1: When Billy looked under the boxes in the beginning,
where was the dog?
Memory 2: Where did the dog go after that?
Reality: Where is the dog now?

Think: Where does Billy think the dog is?
Prediction: Which box will Billy go to with the bone?
Appendix 2
Cartoon used in Experiment 7.
977 977
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A developmental shift in processes underlying successful belief-
desire reasoningApproach and avoidance FB tasksSelection
ProcessingSelection Processing in avoidance FB tasksThe
Inhibition of Inhibition modelExperiments 1-
5MethodSubjectsMaterialsProcedureExperiment 1Experiment
2Experiments 3-5ResultsDiscussionExperiment
6MethodSubjectsProcedureResultsDiscussionExperiments 7 and
8MethodSubjectsMaterialsProcedureResultsDiscussionGeneral
discussionAcknowledgmentsAppendix 1Appendix 2References

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